Summary: We present a new method to detect weak linear frequency modulated (LFM) signals in strong noise using the chaos oscillator. Chaotic systems are sensitive to specific signals yet immune to noise. With our new method we firstly use the Radon-Wigner transform to dechirp the LFM signal. Secondly, we set up a chaotic oscillator sensitive to weak signals based on the Duffing equation, and poising the system at its critical state. Finally, we input the dechirped sequence into the system as a perturbation of the driving force. A weak signal with the same frequency will lead to a qualitative transition in the system state. The weak signal in the presence of strong noise can then be detected from the phase transition of the phase plane trajectory of the chaotic system. Computer simulation results show that LFM signals with an SNR lower than -27 dB can be detected by this method.